标题： 用于酉矩阵可扩展量子电路近似的量子神经网络框架 显示英文标题

标题： A quantum neural network framework for scalable quantum circuit approximation of unitary matrices

摘要： 在本文中，我们开发了一种李群理论方法，用于酉矩阵的参数表示。 这导致开发了一个量子神经网络框架，用于多量子比特酉门的量子电路近似。 神经网络的层由标准递归块基的某些元素的指数乘积定义，我们将之引入为复矩阵阶数$2^n$的矩阵代数中保罗字符串基的替代方案。 神经网络的递归构造意味着量子电路近似是可扩展的，即： 一个$(n+1)$量子比特酉门的量子电路可以从$n$量子比特系统的电路通过添加几个CNOT门和单量子比特门来构建。 显示英文摘要

摘要： In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of the neural networks are defined by product of exponential of certain elements of the Standard Recursive Block Basis, which we introduce as an alternative to Pauli string basis for matrix algebra of complex matrices of order $2^n$. The recursive construction of the neural networks implies that the quantum circuit approximation is scalable i.e. quantum circuit for an $(n+1)$-qubit unitary can be constructed from the circuit of $n$-qubit system by adding a few CNOT gates and single-qubit gates.